Lecture 20-Slides - Introduction to 8086 Assembly

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Introduction to 8086 Assembly

Lecture 20

x86 floating point

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Floating point operations

● Floating point libraries

● Math coprocessor (floating point coprocessor, floating point unit FPU)

○ add-on

○ Integrated

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Intel 8087 coprocessor

https://en.wikipedia.org/wiki/Intel_8087

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http://www.s100computers.com/My%20System%20Pages/

8086%20Board/8086%20CPU%20Board.htm

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Intel 8087 coprocessor

http://www.s100computers.com/My%20System%20Pages/

8086%20Board/8086%20CPU%20Board.htm

http://7review.com/remembering-maths-coprocessor/

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https://en.wikipedia.org/wiki/Intel_80486SX https://en.wikipedia.org/wiki/Intel_80486

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Intel x87 extended precision

https://en.wikipedia.org/wiki/Extended_precision

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8087 register stack

● ST0, ST1, ST2, ST3, ST4, ST5, ST6, ST7

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8087 register stack

ST7

ST6

ST5

ST4

ST3

ST2

ST1

ST0

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8087 register stack

4.2 6.8 12.0 0.003

ST7 ST6 ST5 ST4

40.9 111.1 12.04 48.88

ST3

ST2

ST1

ST0

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8087 register stack

4.2 6.8 12.0 0.003

ST7 ST6 ST5 ST4

40.9 111.1 12.04 48.88

ST3 ST2 ST1 ST0

push 72.0

6.8 12.0 0.003

ST7 ST6 ST5

ST4 40.9

111.1 12.04 48.88

ST3 ST2 ST1

ST0 72.0

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8087 register stack

https://users.pja.edu.pl/~jms/qnx/help/watcom/compiler16/pragma16.html

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Floating points in memory

single precision

double precision

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Floating points in memory

32 bit integer

double precision

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Example

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Example

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Loading (pushing)

FLD mem32 (/mem64/mem80) push ST0 <- mem32 (so on)

FLD STi push ST0 <- STi

STi: ST0, ST1, … or ST7

FILD mem16 (/mem32/mem64) push ST0 <- int2float(mem32)

Example:

FLD dword [l1]

FLD qword [l2]

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Loading (pushing) constants

FLD1 push ST0 <- 1.0

FLDZ push ST0 <- +0.0

FLDPI push ST0 <- π (the pi number) FLDL2T/FLDL2E

FLDLG2/FLDLN2

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Storing

FST mem32/mem64 mem32 <- ST0

FST STi STi <- ST0 (i=0,1,...,7) FIST mem16/mem32/mem64 mem32 <- float2int(ST0) FSTP dest

FISTP dest

similar to FSTP and FISTP but also pops top of stack

Example:

FST dword [l1]

FST qword [l2]

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Exchange

FXCH STi ST0 <-> STi (i=0,1,...,7)

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Math operations

FADD src ST0 += src

FSUB src ST0 -= src

FMUL src ST0 *= src

FDIV src ST0 /= src

src: STi/mem32/mem64

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Math operations

FADD src ST0 += src

FSUB src ST0 -= src

FMUL src ST0 *= src

FDIV src ST0 /= src

FSUBR src ST0 = src - ST0

FDIVR src ST0 = src / ST0

src: STi/mem32/mem64

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Math operations

FADDP STi STi += ST0

FSUBP STi STi -= ST0

FMULP STi STi *= ST0

FDIVP STi STi /= ST0

FSUBRP STi STi = ST0 - STi

FDIVRP STi STi = ST0 / STi

And pop top of stack

STi: ST0, ST1, … or ST7

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Math operations

FADDP STi

FADDP STi, ST0 STi += ST0

FSUBP STi

FSUBP STi, ST0 STi -= ST0

FMULP STi

FMULP STi, ST0 STi *= ST0

FDIVP STi

FDIVP STi, ST0 STi /= ST0

FSUBRP STi

FSUBRP STi, ST0 STi = ST0 - STi

FDIVRP STi

FDIVRP STi, ST0 STi = ST0 / STi

And pop top of stack

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Math operations

FADD STi, ST0 STi += ST0 FSUB STi, ST0 STi -= ST0 FMUL STi, ST0 STi *= ST0 FDIV STi, ST0 STi /= ST0

FSUBR STi, ST0 STi = ST0 - STi FDIVR STi, ST0 STi = ST0 / STi

STi: ST0, ST1, … or ST7

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Math operations

FIADD src ST0 += int2float(src) FISUB src ST0 -= int2float(src) FIMUL src ST0 *= int2float(src) FIDIV src ST0 /= int2float(src)

FISUBR src ST0 = int2float(src) - ST0 FIDIVR src ST0 = int2float(src) / ST0

src: mem32/mem64

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Example

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Math operations

FCHS ST0 = -ST0

FABS ST0 = |ST0|

FSQRT ST0 = sqrt(ST0)

FSCALE ST0 *= 2^floor(ST1)

FRNDINT ST0 = round(ST0)

still floating point

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Math operations

FSIN ST0 = sin(ST0)

FCOS ST0 = cos(ST0)

FSINCOS ST0 = cos(ST0)

then ST0 <- push sin(ST0)

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x87 status register

http://www.russinoff.com/libman/text/node48.html

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Making comparisons

FCOM src compare ST0, src

src: mem32/mem64/STi

FCOMP src like FCOM src

AND pop top of stack

FCOMPP Compare ST0, ST1

AND pop twice

FICOM mem16/mem32 compare ST0, int2float(src) src: mem32/mem64/STi

FTST compare ST0, 0

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Making comparisons

FSTSW mem16 FSTSW AX

SASF FLAGS <- AX

(not all bits)

LASF AX <- FLAGS

(not all bits)

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Making comparisons

FSTSW mem16 FSTSW AX

SASF FLAGS <- AX

(not all bits)

LASF AX <- FLAGS

(not all bits)

FSTSW AX SASF

follows every comparison

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Directly setting EFLAGS

FCOMI STi compare ST0, STi sets EFLAGS

FCOMIP STi FCOMI STi

pops top of stack

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Practice: roots of a quadric

extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

no_roots_msg: db "No real roots",10, 0

segment .text :

quadroots.asm

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Practice: roots of a quadric

extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

segment .text :

fld qword [b]

fmulp ST1

quadroots.asm

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Practice: roots of a quadric

extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

segment .text :

fld qword [b]

fmulp ST1

fld qword [a]

fld qword [c]

fld qword [minus4]

fmulp ST1 fmulp ST1

quadroots.asm

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extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

segment .text :

fld qword [b]

fld qword [b]

fmulp ST1

fld qword [a]

fld qword [c]

fmulp ST1 fmulp ST1 faddp ST1 fldz

fcomip ST1 ja no_roots

quadroots.asm

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extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

no_roots_msg: db "No real roots",10, 0 segment .text

:

fld qword [b]

fmulp ST1

fld qword [a]

fld qword [c]

fmulp ST1 fmulp ST1 faddp ST1

fldz

quadroots.asm

fsqrt

fld st0 fld qword [b]

faddp st1 fchs

fld qword [a]

fld1 fld1 faddp fmulp

fdivp ST1 ; ST1 /= ST0

; print st0

fst qword [temp]

push dword [temp+4]

push dword [temp]

push format call printf add esp, 12 fcomp

fld qword [b]

fchs faddp

fld qword [a]

; print st0

push format call printf add esp, 12

jmp endl

no_roots:

mov eax, no_roots_msg call print_string

endl:

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extern printf segment .data a: dq 1.0 b: dq -3.0 c: dq 2.0 minus4: dq -4.0 temp: dq 0.0 format: db "%f", 10, 0

no_roots_msg: db "No real roots",10, 0 segment .text

:

fld qword [b]

fmulp ST1

fld qword [a]

fld qword [c]

fmulp ST1 fmulp ST1 faddp ST1

fldz

quadroots.asm

fsqrt

fld st0 fld qword [b]

faddp st1 fchs

fld qword [a]

fdivp ST1 ; ST1 /= ST0

; print st0

push format call printf add esp, 12 fcomp

fld qword [b]

fchs faddp

fld qword [a]

; print st0

push format call printf add esp, 12

jmp endl

no_roots:

mov eax, no_roots_msg call print_string

endl:

This code is inefficient!

Go through the code and make it

more efficient.